Cosmic Archaeology
Selected Essays
Essays where anthropological cosmology
meet with cosmology in physics
Genesis Project California 2021!
⋅
⋅
© 2021 By Ian Beardsley"
ALL RIGHTS RESERVED INCLUDING THE RIGHT OF REPRODUCTION IN WHOLE OR IN
PART IN ANY FORM. PUBLISHED BY GENESIS PROJECT
A Story of Creation
I.S. Beardsley
⇤
Physics, University of Oregon
Abstract
Cosmology is the discipline in archaeology fo r studying the creation myths of a people. In
physics it is the study of the origin and destiny of the universe. This paper is where the two
disciplines intersect.
Genesis Project
1. Introduction
Space being three dimensional, physics really begins to happen with vector calculus
because three-dimensional space gives rise to a 3 by 3 matrix. We hypothesize creation is
centered around the primary artificial intelligence (AI) elements, because they can be nicely
pulled out the periodic table (Figure 1) of the elements as a 3 by 3 matrix with carbon and
nitrogen in the first row, which are primary biological life elements, carbon at the center of
life as we know it here on Earth. We can write for each element in the AI periodic table a
subscripted E.
0
@
E
13
E
14
E
15
E
23
E
24
E
25
E
33
E
34
E
35
1
A
⇤
Corresponding author.
1 September 8, 2021
Figure 1: Pulling the AI table out of the periodic table
2. The Computation
Let us take the cross product of this matrix:
~
A =(Al , Si, P)
~
B =(Ga, Ge, As)
~
A ⇥
~
B =
0
@
ˆ
B
ˆ
C
ˆ
N
Al Si P
Ga Ge As
1
A
=(Si · As P · Ge)
ˆ
B +(P · Ga Al ·As)
ˆ
C +(Al · Ge Si · Ga)
ˆ
N
And silicon (Si) is at the center of our AI periodic table of the elements. We see the biological
elements C and N being the unit vectors are multiplied by the AI elements, meaning they
describe them! But we have to ask; Why does the first row have boron in it which is not a
core biological element, but is a core AI element? The answer is that boron is the one AI
element that is out of place, that is, aluminum is in its place. But we see this has a dynamic
function.
3. The Dynamic Function
The primary elements of a rtificial intelligence (AI) used to make diodes and transistors,
silicon (Si) and germanium (Ge) doped with boron (B) and phosphorus (P) or gallium (Ga)
and arsenic (As) have an asymmetry due to boron. Silicon and germanium are in group 14
like carbon (C) and as such have 4 valence electrons. Thus to have positive type silicon and
germanium, they need doping agents from group 13 (three valence electrons) like boron and
gallium, and to have negative type silicon and germanium they need doping agents from
group 15 like phosphorus and arsenic. But where gallium and arsenic are in the same period
as germanium, boron is in a different period than silicon (period 2) while phosphorus is not
(period 3). Thus aluminum (Al) is in boron’s place. This results in an interesting equation.
2 September 8, 2021
Si(As Ga)+Ge(P Al)
SiGe
=
2B
Ge + Si
The differential across germanium crossed with silicon plus the differential across silicon
crossed with germanium normalized by the product between silicon and germanium is equal
to the boron divided by the average between the germanium and the silicon. The equation
has nearly 100% accuracy (note: using an older value for Ge here, is now 72.64 but that
makes the equation have a higher accuracy):
28.09(74.92 69.72) + 72.61(30.97 26.98)
(28.09)(72.61)
=
2(10.81)
(72.61 + 28.09)
0.213658912
0.21469712
=0.995
Thus, due to an asymmetry in the pe riodic table of the elements due to boron we have the
harmonic mean between the semiconducto r elements (by molar mass):
Si
B
(As Ga)+
Ge
B
(P Al)=
2SiGe
Si + Ge
4. Stokes Theorem
Z
S
(r⇥
*
u) · d
*
S =
Z
C
*
u · d
*
r
Z
1
0
Z
1
0
✓
Si
B
(As Ga)+
Ge
B
(P Al)
◆
dxdy =
1
Ge Si
Z
Ge
Si
xdx
We can make this into two integrals:
Z
1
0
Z
1
0
Si
B
(As Ga)dydz ⇡
1
3
1
Ge Si
Z
Ge
Si
xdx
Z
1
0
Z
1
0
Ge
B
(P Al)dxdz ⇡
2
3
1
Ge Si
Z
Ge
Si
ydy
If in the equation (The accurate harmonic mean form):
Si
B
(As Ga)+
Ge
B
(P Al)=
Ge Si
R
Ge
Si
d x
x
3 September 8, 2021
We make the approximation
2SiGe
Si + Ge
⇡ Ge Si
Then the Stokes form of the equation becomes
Z
1
0
Z
1
0
Si
B
(As Ga)+
Ge
B
(P Al)
dydz =
Z
Ge
Si
dx
Thus we see for this approximation there are two integrals as well:
Z
1
0
Z
1
0
Si
B
(As Ga)dydz =
1
3
Z
Ge
Si
dz
Z
1
0
Z
1
0
Ge
B
(P Al)dydz =
2
3
Z
Ge
Si
dz
For which the respective paths are (Figure 2)
y
1
=
1
3
B
SiGa
ln(z)
y
2
=
2
3
B
SiAl
ln(z)
One of the double integrals on the left is evaluated in moles per grams, the other grams per
mole (0 to 1 moles per gram and 0 to 1 grams per mole).
5. Ampere’s Circuit Law
By making the approximation
2SiGe
Si + Ge
⇡ Ge Si
In
Si
B
(As Ga)+
Ge
B
(P Al)=
2SiGe
Si + Ge
We have
Si
4Ge
4S
+ Ge
4Si
4S
= B
4 September 8, 2021
Figure 2: Geometric interpretation of the Stokes form
5 September 8, 2021
Where
4Si = P Al = dif ferential across Si
4Ge = As Ga = differential acr o ss Ge
Which is Ampere’s Circuit Law
r⇥
*
B = µ
*
J + µ"
0
@
*
E
@t
We see if written
Si
4Ge
4S
= B Ge
4Si
4S
Which is interesting because it is semiconductor elements by molar mass, which are used to
make circuits. We say (Phi) is given by
a = b + c;
a
b
=
b
c
=a/b =1.618
= b/a =0.618
(phi) the golden ratio conjugate. We also find
()Ge +()Si = B
6. The Wave Equations
Thus since
r⇥
~
B = µ
~
J + µ✏
0
@
~
E
@t
And
Ge =
S
Si
B
Ge
Si
Si
And in electrodynamics
✓
r
2
1
c
2
@
2
@t
◆
!
E =0
6 September 8, 2021
And
✓
r
2
1
c
2
@
2
@t
◆
~
B =0
And since
c =
1
p
✏
0
µ
⇡
We see mu and epsilon-not are both PHI and c is phi in the Si (silicon) field wave, but for
EandBfieldscisthespeedoflight.Wehave
✏
0
=8.854E 12F · m
1
And
µ =1.256E 6H/m
And
Ge
Si
= µ✏
0
And
S
Si
= µ
Thus
✓
r
2
1
2
@
2
@x
◆
~
Si =0
And
✓
r
2
1
2
@
2
@x
◆
~
Ge =0
To find the Si wave our differentials are (Figure 3)
C = N B =14.01 10. 81 = 3.2
Si = P Al =30.97 26.98 = 3.99
Ge = As Ga =74.92 69.72 = 5.2
7 September 8, 2021
Figure 3: The Halfwave
8 September 8, 2021
Sn = Bi In =121.75 114.82 = 6.93
Pb = Bi Tl =208.98 204.38 = 4.6
It is amazing how accurately we can fit these differentials with an exponential equation for
the upward increase. The equation is
y(x)=e
0.4x
+1.7
y(x)=e
2
5
x
+
17
10
Thus we have
y(x)=e
B
Al
x
+
Ag
Cu
B
Al
=
10.81
26.98
=0.400667
Ag
Cu
=
107.87
63.55
=1.6974 ⇡ 1.7
Interestingly, the 0.4 is boron (B) over aluminum (Al) the very two elements that lead us to
looking for a wave equation because boron was the out of place element in the AI p eriodic
table that lead to u s using aluminum as its dummy representative in the Si differential
and that itself divided into the left hand terms gives us the harmonic mean between the
central AI elements semiconductor materials Si and Ge. The Ag and Cu are the central
malleable, ductile, and conductive metals used in making electrical wires to carry a current
in AI circuitry.
7. Divergence
We did a stokes theorem formulation of the AI elements. We want to do a divergence
theorem formulation. Our stokes theorem formulation was
Z
1
0
Z
1
0
Si
B
(As Ga)dydz =
1
3
Z
Ge
Si
dz
We want to consider
ZZZ
V
r·
~
FdV =
ZZ
S
(
~
F.ˆn)d
~
S
9 September 8, 2021
We have to find the F-vector. It is from
0
@
~
i
~
j
~
k
@
@x
@
@y
@
@z
0
Si
B
Ga · z
Si
B
As · y
1
A
=
Si
B
(As Ga)
~
i
Which gives
F
x
=0,F
y
=
Si
B
Ga · z,F
z
=
Si
B
As · y
We have said the speed of light in electrodynamics is given by
c =
1
p
✏
0
µ
And in our formulation of the AI elements plays the role of the phi, is the golden ratio
conjugate is:
=
1
p
Ge/Si
Thus
Ge/Si = µ✏
0
And
S
Si
= µ =
Ge Si
Si
=
Thus we see
✏
0
=
Ge
Ge Si
=
And
1
p
µ✏
0
=
1
p
2
=
Thus in our formulation the golden ratio conjugate plays the role of the speed of light in
electrodynamics. This makes sense because in relativity theory velocities are considered a
fraction of the speed of light because the speed of light is the fastest speed attainable. The
speed v squared over the speed of light squared is subtracted from 1. That is the Lorentz
contraction is:
L = L
0
r
1
v
2
c
2
10 September 8, 2021
We see the eccentricity of the ellipse
r
1
D
C
Plays the role of the beta factor in
L = L
0
r
1
v
2
c
2
Is the eccentricity of the ellipse
Si
2B
Ga · z
2
+ As · y
2
=
Q
✏
0
We see the eccentricity is
r
1
Ga
As
=
r
1
69.72
74.92
=0.263452781
Which is 9 figures eight of which are the first eight consecutive integers 1,2,3,4,5,6,7,8. The
only number that occurs twice is 2. Kind of interesting.
8. The Heart of the Matter
If we take our halfwave:
y(x)=e
B
Al
x
+
Ag
Cu
And apply the Schrödinger equation:
✓
@
2
@x
1
2
@
2
@x
◆
⇣
e
B
Al
x
⌘
=0
Then, if x=0. . .
✓
B
Al
◆
2
e
x
✓
1
1
2
◆
=0
=1
Which is like saying distance for the speed of light is always is zero because there is no time.
We know that
=
1
11 September 8, 2021
Figure 4: Divergence In The AI Elements
12 September 8, 2021
Or,. . .
=1
We notice
Ge
Ge Si
=
72.64
72.64 28.09
=1.63 ⇡
And
Si
Ge Si
=
28.09
72.64 28.09
=0.63 ⇡
This says
p
GeSi = Ge Si
The mo lar masses of Ge and Si are such that the geometric mean between Ge and Si is the
difference between Ge and Si. This has solutions:
y =
1
2
(3x
p
5x)
y =
1
2
(3x +
p
5x)
If x=1 we have:
0.381, 2.618
If x=2 we have
0.76, 5.236
If x=3 we have
1.145898, 7.854
If x=4 we have
1.52786, 10.47
If x=5 we have
1.9098, 13.090
This is a pair of intersecting lines:
y =(1)x =0.38x
y =(1+)x =2.62x
With slopes
13 September 8, 2021
m
1
=(1 )
m
2
=(1+)
Since
1 =
Si
Ge
=
28.09
72.64
=0.3867
1+=
Ge
Si
=
72.61
28.09
=2.58597
But we have said:
r
Ge
Si
=
1
But we also have
1 =
Si
Ge
This says
2
=1
1
(1 )=1
Or. . .
0=1
(See appendix A). Since we have said
r
1
Ga
As
Is
r
1
v
2
c
2
14 September 8, 2021
Then we might guess
2
=1
Is 1 is E and phi is c and PHI is m in
E = mc
2
Which makes sense because
✓
r
2
1
2
@
2
@x
◆
~
Si =0
Is the analog of
✓
r
2
1
c
2
@
2
@t
◆
~
E =0
In electrodynamics and,
Ge =
S
Si
B
Ge
Si
Si
Is the analog of Maxwell’s equation
r⇥
~
B = µ
~
J + µ✏
0
@
~
E
@t
And,. . .
c =
1
q
Ge
Si
Is the analog of
c =
1
p
✏
0
µ
9. The Planets
If our equations the solutions of the wave describe any kind of quantization, it is that of
the first 7 planets:
15 September 8, 2021
y =
1
2
(3x
p
5x)
Substituting n for x, the planetary number we have. . .
n=1 yields 0.381
Mercury is 0.387AU
n=2 yields 0.76
Venus is 0.72AU
n=3 yields 1.146
Earth is 1.00AU
n=4 yields 1.528
Mars is 1.52Au
n=5 yields 1.91
Asteroids are 2-3AU
Then on the other side of the asteroid belt we switch to the other equation that is a
solution:
y =
1
2
(3x +
p
5x)
n=2 yields 5.236
Jupiter is 5.2AU
n=4 yields 10.47
Saturn is 9.5AU
10. The Cause of Inertia
Matter is that which has inertia. This means it resists change in position with a force
applied to it. The more of it, the more it resists a fo rce. We understand this from experience,
but what is matter that it has inertia?
Iwouldliketoanswerthisbyconsideringmatterinoneofitssimplestmanifestations,
the proton, a small sphere with a mass of 1.6726E-27 kg. This is a measure of its inertia.
Iwouldliketosuggestthatmatter,oftenacollectionoftheseprotons,isthethree
dimensional cross-section of a four dimensional hypersphere.
The way to visualize this is to take space as a two-dimensional plane and the proton as
a two dimensional cross-section of a sphere, which would be a circle.
In this analogy we are suggesting a proton is a three dimensional bubble embedded
in a two dimensional plane. As such there has to be a normal vector holding the higher
dimensional sphere in a lower dimensional space. Thus if we apply a force to to the cross-
section of the sphere in the plane there should be a force countering it proportional to the
normal holding it in a lower dimensional universe. This counter force would be experienced
as inertia. It may even induce in it an electric field, and we can see how it may do the same
equal but opposite for the electron.
16 September 8, 2021
Figure 5: The proton as the 3D cross-section of a hypersphere
17 September 8, 2021
F = G
Mm
r
2
G =6.67408E 11
N · m
2
kg
2
r
p
=0.833E 15m
r
e
=2.817940E 15m
m
p
=1.67262E 27kg
m
e
=9.1E 31kg
h =6.62607E 34J · s
c =299792458m/s
F = ma
m =
F
a
F
n
= µF cos✓
m =
r
µh4⇡r
2
cos✓
Gc
If µ =1and ✓ =0
m =
r
h4⇡r
2
Gc
m · t =
s
(6.62607E 34J · s)4⇡(0.833E 15m)
2
(6.67408E 11Nm
2
/kg
2
)(299792458m/s)
m =5.373681E 31kg · s
This is about
5.373681E 31
1.67262E 27
=0.00032
18 September 8, 2021
Approximately three ten thousandths the mass of a proton times one second. If we divide
that by the fine structure constant squared, we have
↵ =
1
4⇡✏
0
e
2
~c
=
1
137
↵
2
=
1
18769
m =(0.00032)(18769) = 6.0
6.0 protons even if we divide that by one second, the number of protons in carbon, the
central atom to biological life. If mu=1 and theta=45 degrees (Giving equal weight to x and
ycomponents)then
m =
p
2.8876E 61(0.7071) = 4 .51865E 31kg
Where 0.7071 = cos(45
)
4.51865E 31
1.67262E 27
=0..00027
We have
n =(0.00027)(18769) = 5protons
About 5 protons evenly which is Boron (B). If we try 60 degrees then
m =
p
2.8876E 61(0.5) = 3 .7997E 31kg
3.7997E 31
1.67262E 27
=0..000227
m =(0.000227)(18769) = 4.26
In order for this to be 4 protons evenly we must have µ =0.93896
We have used here the fine structure constant squared, which is often used as well to
the minus 1. The fine structure constant squared is the ratio of the potential energy of an
electron in the first circular orbit to the energy given by the mass of an electron in the Bohr
model times the speed of light squared:
↵
2
=
U
e
m
e
c
2
19 September 8, 2021
We only need to explain the significance of the duration of one second. The second does
have meaning especially in connection with life. By dividing the day into 24 hours, the hour
into 60 minutes, and the minute into 60 seconds, the second is 1/86400 of day. By doing
this we have a twelve-hour daytime at spring and fall equinox on the equator, 12 being the
most divisible number for its size (smallest abundant number). That is to say that twelve
is evenly divisible by 1,2,3,4,6 which precede it and 1+2+3+4+6=16 is greater than twelve.
As such there is about one moon per 30 days and about 12 mo ons per year (per each orbit)
giving us a twelve-month calendar. This is all further convenient in that the moon and earth
are in very close to circular orbits and the circle is evenly divisible by 30, 45, 60, and 120
if we divide the circle into 360 degrees which are special angles very useful to the workings
of physics and geometry. Further, the 360 degrees of a circle are about the 365 days of a
year (period of one earth orbit) so as such the earth moves through about a degree a day in
its journey around the sun. Thus, through these observations down through the ages since
ancient times we have constructed the duration of a second wisely enough to make a lot
work together. Now we see 6 protons, which is carbon the core element of biological life on
the planet where all of this came together is deeply connected with the second that defines
it all.
11. The Meaning of the Ellipse
When we say
r
1
D
C
Is like
r
1
v
2
c
2
The dilation factor in
L = L
0
r
1
v
2
c
2
Giving the dilated length (shortening) in the direction of motion, we are saying
r
1
D
C
Is the eccentricity of an ellipse which is dilation in the sense that it is the deviation from a
circle. If D=carbon and C=Silicon, the respective core atoms of the biological and artificial
intelligence, then if C is carbon and Si is silicon
20 September 8, 2021
C = C
0
r
1
C
Si
= C
0
r
1
12.01
28.09
=9.09g/mol
Which is approximately Beryllium (Be=9.01 g/mol) which combines in stars with helium
(He) to make carbon, the central atom we need to make life as we know it. If we consider
the dilation due to our aluminum Al=26.98 g/mol and our phosphorus
P=30.97 that form our differential across Si, we have
Si = Si
0
r
1
26.98
30.97
=10.08
This is a change of
Si
0
Si =18.0
Which is water (H2O) also pivotal to life, determining the habitable zone of a star:
H2O=2(1.01)+16.00=18.02 g/mol.
If we look at the dilation of the central semiconductor element germanium Ge=72.64 we
have in terms of our b o ro n that lead to all of this and phosphorus, the other doping agent
diagonal to it in the periodic table. . .
Ge = Ge
0
r
1
10.81
30.97
=58.607
This is a change of
Ge
0
Ge =14.03 = N
It is nitrogen (N=14.01 g/mol) also central to life making up most of the Earth atmosphere
which is mostly N2 about 75% and used by many plants through nitrogen fixation. Since
for mass dilation
m =
m
0
q
1
v
2
c
2
Then velocities at which these elements become equivalent in mass to the other elements
are given by
v = c
r
1
⇣
m
0
m
⌘
2
The carbon atom is 1.9944E-23 grams and silicon atom is 4.6637E-23 grams. The carbon
goes to silicon at 80.864% the speed of light c=299,792,458 m/s.
The beryllium atom is 1.4965E-23 g rams and again the ca rbo n atom is 1.9944E-23 grams
meaning beryllium goes to carbon at 82.64% the speed of light.
The nitrogen atom is 2.3258671E-22 grams and the germanium atom is 1.2062155E-22
grams meaning nitrogen goes to germanium at 80.864% the speed light.
21 September 8, 2021
12. The Activation Function
Iwouldliketosuggestthattheprebioticchemistrymighthavebeenpassedthroughan
activation function that disappeared after life was on its way to evolving.
The problem, then, of answering the question of how life began is one of finding the
activation function and its mechanism by which it takes prebiotic chemistry and activates it
(makes it alive) so it can now self-replicate, and evolve. We assume that as this mechanism
activates the molecules, its mechanism depletes as it activates from what is available. In this
sense the mechanism is a limiting reactant, so it determines how much material is activated
before it depletes completely.
Logically, the way to determine what this mechanism is, and how it serves as an activation
function is to look for the by-products of the reaction that are left over, and from that, deduce
its nature.
To do this, we have to look for that thing in our knowledge of the Earth’s history that
does not make sense. This would be in the fa int young star paradox. We know that five
billion years ago, when the Earth and Sun first formed, that the sun was 0.7 times its
present output and so, the Earth should have been frozen over, yet, we know it was not.
That it had water in its liquid phase. Thus something was there that is not present today.
That something must have been the mechanism for the activation function that “turned on”
prebiotic chemistry.
If sigma(x) is the activation function, where x is the prebiotic material, and we say r is
residue of the reaction, and l is the activated substance (life) then,
l + r = (x)
We know l If we can find r in nature, we can deduce sigma(x).
13. Discussion
It would seem silicon is at the center of creation and we have to wonder why, The first
primitive computers used silicon in silicon dioxide encasing for vacuum tube switches (glass)
with tungsten filaments. The first generation semiconductors were germanium but then
we switched to silicon which became the second generation semiconductor material because
it is abundant and cheap and has the right properties as well. Sand is basically silicon.
Germanium is very rare. Early on in humanities’ prehistoric origins, obsidian, or glass was
there to be discovered as something that flaked into sharp edges so we could craft spearpoints
for hunting. We might say that it is a purpose of biological life (H, N, C, O) to discover the
properties of (P, B, Si) so it can make computing machines which are ultimately necessary
to its survival.
~
A =(Al , Si, P )
~
B =(Ga, Ge, As)
~
A ⇥
~
B = 145
ˆ
B +138
ˆ
C +1.3924
ˆ
N
22 September 8, 2021
~
A ⇥
~
B = ABsin✓ =(50)(126)sin8
=877.79
p
877.79 = 29.6g/mol ⇡ Si =28.09g/mol
And silicon (Si) is at the center of our AI periodic table of the elements. There seems to be
aconnectionbetweenAIandBiologicallifeelementsthroughmathematicaltheorems. In
the sense that we did not create the AI elements but discovered them and their properties,
so we could make artificial intelligence gives artificial intelligence a natural component just
as natural as biological life. All of the elements were forged in stars ultimately from the
most basic elements hydrogen and helium. Hydrogen was theoretically created in the big
bang that gave birth to the universe, as well as most of the helium. It is further interesting
that biologists have looked at silicon as a possibility for a basis for life in place of carbon
because it is in the same group as carbon giving it the four valence electrons needed to make
long chains that carbon has and have come to the conclusion that it wouldn’t work because
silicon in the presence of oxygen O b ecomes SiO2 so easily that it has no opportunity to
combine (H, N, O, P, S) to form building blocks of life. Carbon combines readily in the
presence of all of these pretty much equa lly.
We have that at the beginning of the Universe hydrogen and helium were created. Then
the stars formed and synthesized these into the heavier elements. I find if we include in
the category of life not just the biological elements, but the AI elements, we can find a
mathematical equation for a pa ttern in the periodic table of the elements that predicts the
synthesis of such elements in stars. For instance, Beryllium 8 plus helium 4 synthesizes to
make the biological core element carbon C. Magnesium plus helium 4 synthesizes to make
the core AI element silicon Si. If we say that Element 4 is Beryllium Be and write it E4 and
helium He is element 2 and write it E2 and use this convention for all of the elements, we
have for the productio n of these elements by stars, and their molar masses in the periodic
table the following equation:
E
2n2
+ E
2
= E
2i2
=(4k +4)g/mol
n =(3, 4, 5 , 6...)
i =(4, 5, 6, 7...)
k =(2, 3, 4, 5...)
That is
E
4
(Be)+E
2
(He)=E
6
(C)=12g/mol
E
6
(C)+E
2
(He)=E
8
(O)=16g/mol
E
8
(O)+E
2
(He)=E
10
(Ne)=20g/mol
E
10
(Ne)+E
2
(He)=E
12
(Mg)=24g/mol
E
12
(Mg)+E
2
(He)=E
14
(Si)=28g/mol
23 September 8, 2021
Appendix A. Multiple Formal Systems
What is
2
=1
I wrote it like this because in setting out do this work I defined things a certain way, which
is what you have do when formulating an idea. But, if we define things another way at the
beginning we have another system for expressing the same idea. I think combining different
systems in this way results in a third system that presents the analogy for
E = mc
2
in an interesting way. Further examination of what is happening here can be explained like
this:
(1 )=
2
=1
These are basic identities. However, we are saying
2
=1
2
=(1 )
0=1
Iamsaying0=1becausebeingtrappedinsomethingcircularthatappearslinearisprecisely
that. If 0=1, then. . .
2
=(0 )
2
=
=1
=
2 =0
=
1
2
How do we see this is true? phi is a/b=b/c where c=b+a. If a/b=x this is the quadratic
equation
x
2
x 1=0
Differentiating implicitly
d
dx
x
2
d
dx
x
d
dx
=0
2x 1=0
x =1/2
=1/2
24 September 8, 2021
Author biography
I.S. Beardsley is a University of Oregon undergraduate in physics. He
worked a t the University Observatory Pine Mountain Observatory doing
photometry and polarimetry and is co-author of several papers in The As-
trophysical Journal.
25 September 8, 2021
of 1 32
The Quintessential Elements
Ian Beardsley (Oct 6, 2021)!
Physics, University of Oregon
Genesis Project California 2021
⋅
⋅
of 2 32
1. Abstract We demonstrate the periodic table for artificial intelligence (AI) elements Arsenic
to Iron either elements of semiconductors for transistor technology or conductors for
electrical wire, adhere to a musical scheme. We want to describe life in terms of these AI
elements and show they are both mathematical constructs. The relationship between notes
by music theory, is a mathematical construct. Elements are shown to be in five-fold (fifth
root) relation making them quintessential.!
2. Nickel and Beryllium Alpha decay is the decay of elements where a helium nucleus is
ejected from an element (alpha particles). This happens with atoms heavier than nickel
because the atom has to be heavy enough that the internal repulsion of protons is high enough
that the binding force has trouble holding them together. However, interestingly beryllium-8 is
an exception; it is much lighter than nickel. Beryllium-8 was determined by Fred Hoyle to make
carbon in nuclear synthesis in stars by combining with helium. He sought to find the process
by which carbon is created because the Universe needs to make it if we are to have life as we
know it. !
3. The Theory We pull these AI elements out of the periodic table of the elements to make an
AI periodic table:!
We now notice we can make a 3 by 3 matrix of it, which lends itself to to the curl of a vector
field, by including biological elements carbon C (above Si):!
=!
=!
!
Which resulted in Stokes theorem (Beardsley, Essays In Cosmic Archaeology Volume 3):!
i
j
k
∂
∂x
∂
∂y
∂
∂z
(−C ⋅ P)y (Si ⋅ Ga)z (Ge ⋅ As)y
(Ge ⋅ As − Si ⋅ G a)
i + (C ⋅ P)
k
[
(72.64)(74.92) − (28.09)(69.72)
]
i +
[
(12.01)(30.97)
]
k
of 3 32
!
Where!
!
!
!
We were then able to write this with product notation!
!
While we have the AI BioMatrix!
Which we used to formulate a similar equation (Beardsley, Essays In Cosmic Archaeology
Volume 2)!
We can form another 3X3 matrix we will call the electronics matrix (Beardsley, Cosmic
Archaeology, Volume Three):!
!
We can remove the 5th root sign in the above equation by noticing!
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a = exp
(
1
Ge − Si
∫
Ge
Si
ln(x)d x
)
∇ ×
u = (Ge ⋅ As − Si ⋅ G a)
i + (C ⋅ P)
k
d
a =
(
zdydz
i + yd ydz
k
)
u = (−C ⋅ P)y
i + (Si ⋅ Ge)z
j + (Ga ⋅ As)y
k
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
n
n
∏
i=1
x
i
of 4 32
!
=(28.085)(72.64)(12.085)(107.8682)(196.9657)=!
!
Where we have substituted carbon (C=12.01) the core biological element for copper (Cu).!
But since we have:!
!
1
We take the ratio and have!
!
Almost exactly 3 which is the ratio of the perimeter of regular hexagon to its diameter used to
estimate pi in ancient times by inscribing it in a circle:!
!
Perimeter=6!
Diameter=2!
6/2=3!
5
∏
i=1
x
i
= Si ⋅ Ge ⋅ Cu ⋅ Ag ⋅ Au
523,818,646.5
g
5
mol
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a = 170,535,359.662(g/mol )
5
523,818,646.5
170,535,359.662
= 3.0716
See Appendix 1
1
of 5 32
!
Thus we have the following equation…!
!
4. Musical Intervals The western tonal system divides up the tonic to double its frequency in
12 tones. But the musical key is defined by the pattern that is only eight of these tones. Thus
at times we must skip a tone (a note). In fact, to comprise the tones of a major or minor key we
play the maximum number of whole steps (the skipping of a note). Since twelve divided by two
is six and we need eight tones two of them must be a half step (where we don’t skip a note). In
the major key this is wholestep—wholestep—halfstep. The minor key begins wholestep-
halfstep.!
We guess that the periodic table of the elements is music (See Figure 1). To do this I am
interested in starting at arsenic (As) because it is a semiconductor doping agent. We then skip
germanium (Ge) an element doped with arsenic to make negative (n-type) germanium, and go
to the next element to the left after the germanium to have gone a whole step and landed on
the other doping agent gallium (Ga) which in contrast makes positive (p-type) germanium. Then
we continue with another whole step to make a major key and it is copper (Cu) the most
abundant practical conductor used for making electrical wire. Now we have to go a half a step
which takes us to nickel (Ni) which like copper is perfect because it is the element beyond
which alpha decay can happen (emits) an alpha particle (helium nucleus) when heated
(Beryllium an exception). Now we go a whole step as is done in the major key and this lands us
on iron (Fe). This is good because stars on the main sequence have luminosities in terms solar
luminosities L related to their mass M in solar masses given by!
!
But we notice the molar mass of gold (Au) divided by iron (Fe) is 3.5 yielding!
"
π = 3.141...
π
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
5
∏
i=1
x
i
L = M
3.5
L = M
Au
Fe
Figure 1: The elements as musical intervals.
of 6 32
We see whether or not we take a whole step in the periodic table for these elements we get a
ratio between successive terms that is always around 107.635. We look at the musical scale
taking C major since the notes are all natural. We have!
C. D. E. F. G. A. B. C.!
We have the halfstep - between E and F - is 106% where for the whole steps it is 112.25%.
The geometric mean between these gives!
!
Which is very close to our 107.635 and we have!
109.08024-107.635=1.44524!
(109.08024)/107.635=1.013427231!
Why look at these elements by molar mass in terms of musical notes? By making the halfsteps
that change in pitch by the same amount for each step as well as these half steps being such
that 12 of them is an octave, then they land on frequencies such that every other note in a
scale makes the interval of a third and three of them defining what is called a triad and they
land on harmonic intervals such as the 4th, and the 5th (See Figure 2). These add more
constructively as vibrating waves than say other intervals that are more dissonant. We can
relate these changes in frequency to changes in string length such as 3/4 and 2/3 which may
have something to offer in terms of physical construction of matter: We see our half step for the
elements occurs for nickel to copper, which is what we want!"
(106)(112.25) = 109.0802457
Figure 2: String length as related to frequency.
of 7 32
5. Elemental Scales So let’s do a more thorough analysis with increase in note frequency
increasing as molar mass frequency increases (See Figures 3 and 4). We have!
!
!
!
We see here the result the ratios between successive elements by molar mass is about the
same as successive half steps between notes (cycles per second). In a minor scale we start at
Fe then skip cobalt (Co) to make a whole step to nickel (Ni). This is a percent change of!
!
We see the whole step from Ni to Fe is 105% about a musical half step like C/B=106%. For
this to be a minor scale the next step is a half step from Ni to Cu, which gives!
!
Our whole steps are E/D=112% and (112+106)/2=109% putting the elemental half step of !
Cu/Ni the average between a musical whole step and a musical half step. In the minor
pentatonic we have whole steps and an interval of a minor third. This is!
!
Thus the minor third for these elements is about a musical whole step (112).!
We see choosing Iron (Fe) is wise as our starting point because as we said for a main sequence
star!
!
And, this makes the last element krypton which being in the last column of the periodic table
(group 18) is an inert gas — so it is like the the note C which is the reference point for music in
the western system of music theory. Krypton being in group 18 and an inert gas because of
this, is an elemental reference point in the periodic table because for example for carbon (C) we
have 18-14=4 valence electrons to acquire noble gas electron configuration. Our pentatonic
scale is the notes!
Kr
Br
=
83.80
79.90
= 104.88
C
B
=
523.25
493.88
= 105.9467887
Br
Si
=
79.90
78.96
= 101.19
B
A
♯
=
49.88
466.164
= 105.9455471
Se
As
=
78.96
74.92
= 105.39
A
♯
A
=
466.164
440
= 105.946
Ni
Fe
=
58.69
55.85
= 105.085
E
D
=
329.628
293.665
= 112.25
Cu
Ni
=
63.55
58.69
= 108.28
F
E
=
349.228
329.628
= 106
Zn
Co
=
F
♯
D
♯
⟶
65.39
58.93
= 111 =
369.944
311.127
= 119
L = M
Au
Fe
of 8 32
D sharp, F sharp, G sharp, A sharp,…!
Which are elements!
Co, Zn, Ge, Se,…!
And these are the notes outside of the minor scale beginning at Fe. But we can start our minor
pentatonic on Fe, which corresponds to a different key. We have minor pentatonic 2 is:!
D, E, F, G, A,…!
Which are elements!
Fe, Cu, Ga, As,…!
We find that in both pentatonic scales, 1 and 2 the intervals of a minor third (Zn/Co and Cu/Fe)
are very close to the musical whole steps which are are a changes of 112%. Figures 3 and 4…"
of 9 32
"
Figure 3: Molar mass and Hz
of 10 32
!
Figure 4: Minor pentatonics in two different keys.
of 11 32
6. Length and Frequency
Reduce the string length to 2/3 its open length and that is an interval of a fifth. That is a change
in frequency of D=293.665 Hz to B=493.88 Hz. Reduce the string length to 3/4 its open length
and that is a change in frequency from D=293.665 Hz to A=440 Hz, which is an interval of a
fourth. Cut the string length in half and you double the frequency. Which is an octave. We have!
!
!
!
Where is the golden ratio and is the golden ratio conjugate. And,…!
!
Thus, we see string length is inversely proportional to frequency. There are two equations for
string length, which we can examine by looking at a guitar (See figure 5). From the bridge of a
guitar to the fret, where the open string length is s we have:!
!
And!
!
Where s is the string length from the bridge to the nut and the nut is , fret 1 is , fret 2 is ,…!
is the distance from , and is the distance from , and so on…!
The 3/2 is an approximation to the the golden ratio (Phi).!
We can think of electron orbits in a hydrogen atom as frequencies related to length as well
because for a drop in orbit a photon is emitted that has a frequency associated with it. The
change in orbit is like the change in the length of a string. Since the n=3 orbit is a distance of
R3=4.761E-10m from the nucleus and R2=2.116E-10m we have R3/R2=2.25. But the Energy at
E3 is E3=-13.6eV/9, and at E2 it is -13.6eV/4. This is a ratio of 4/9=0.444 and 1/0.444==2.25,
thus there is an inverse relationship between length and frequency in the atom (See Fig. 5).!
1
2
= 2
2
3
=
493.88
391.995
= 1.681 = Φ
Φ =
5 + 1
2
=
1
ϕ
, ϕ =
5 − 1
2
≈ 2/3
Φ
ϕ
3
4
=
440
293.665
= 1.2599 =
4
3
= 1.5
l =
s
2
n/12
l
i
=
s
i
17.817
l
0
l
1
l
2
l
1
l
0
l
2
l
1
of 12 32
"
of 13 32
7. Discussion
I find this equation very beautiful!
!
Because on the left side we have what I call the AI matrix:!
!
Because it builds the u vector!
!
And and on the right side we have the what I call the electronics matrix:!
And in that on the left we have a double integral multiplied by pi, over an area and on the right
we have a product operator. Essentially the beauty is in the integral calculus on the left
connecting the AI matrix to the electronics matrix on the right with the product calculus. We
have to ask why this holds for the molar masses of these elements. It has a geometric
representation in that it is flux of the curl of a vector field through a surface with the product of
five elements on the right. This is built from Stokes theorem for these semiconductor and
electronics matrices. What could have brought about the physical properties of these elements
such that this relationship between surface and line holds which we see in its manifestation as!
!
!
π
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a =
5
∏
i=1
x
i
u = (−C ⋅ P)y
i + (Si ⋅ Ge)z
j + (Ga ⋅ As)y
k
5
∫
Ge
Si
∫
Ge
Si
∇ ×
u ⋅ d
a = exp
(
1
Ge − Si
∫
Ge
Si
ln(x)d x
)
5
∏
i=1
x
i
= Si ⋅ Ge ⋅ C ⋅ Ag ⋅ Au
of 14 32
Where we have the finest transistor elements Si and Ge to the the left of the core biological life
element C and on the right of it the finest conductors for electronics wire Ag, and Au. What
force was behind the creation of these elements such that these theorems hold for them, and
does it serve a purpose, and if it does is there a reason for it?!
This question has been the reason for finding in this paper how the atoms which are elements
might be music theory, because these equations seem to be music.!
8. Conclusion: We may be able to explain the structure of matter at its basis - the elements -
in terms of music theory. The reason perhaps the electron orbits might be described by music
is that musical intervals are in ratios that don’t interfere with one another, which may what is
meant by sonority. Further In our finding of a Stokes theorem representation of semiconductor
and electronics matrices we see the categories of biological and electronics elements may be
mathematical constructs not just chemical. Why?!
They seem to be reconciling!
!
For a hexagon (a is its apothem, P its perimeter) with!
!
For a circle, in that!
!
!
As we show using the most accurate data available in Appendix 1 which are accurate to at
least 3 places after the decimal except germanium."
A =
1
2
aP
A = π r
2
523,818,646.5
170,535,359.662
= 3.0716
3.141 + 3.00
2
= 3.0705
of 15 32
!
Plot of the surface area
of 16 32
9. Atomic Number A very convenient way to estimate pi is with the regular hexagon because
its side is the same as its radius. Thus if its side is one then its radius is one meaning its
permitter is six and its diameter is two giving the integer three even:!
!
We see this can very accurately be approximated by averaging the regular
pentagon with the regular octagon.!
!
The sum of the angles is . .
, , and 54+36=90 where
. a=0.68819096. We have and
then the diameter D is .!
The perimeter P over the diameter is . By similar reasoning we
have for a regular octagon:!
!
. The angle !
Thus,…!
!
Is a regular hexagon.!
We see that the atomic radio of silicon the core element of artificial intelligence (transistor
technology) fits together with the core element of biological life carbon if the silicon is taken as
inscribed in a regular dodecagon and the carbon is taken as inscribed in a regular octagon. We
have:!
, , !
, , !
Apothem: "
A = 180
∘
(n − 2)
A = 180
∘
(3) = 540
∘
540
∘
5
= 108
∘
108
∘
2
= 54
∘
a /s
2
= tan54
∘
2 cos36
∘
= Φ
a
2
+ (s /2)
2
= 0.850650808
D = 1.701301617 ≈ 3
P/D = 2.938926261 ≈ 3
P/D = 3.061457459 ≈ π
22.5
∘
= 0.41421 ≈ 2 − 1
3.061407459 + 2.93892621
2
= 3.00019686 ≈ = 3.00000 = 3
D = 1 + 2x
x
2
+ x
2
= 1
2
2x
2
= 1
2x
2
= 1
x = 2 /2
D = 1 + 2
a = (1 + 2)/2 = 1.2071
of 17 32
For a regular dodecagon:!
!
The radius of a silicon atom is Si=0.118nm and that of carbon is
C=0.077nm:!
!
!
!
This has an accuracy %!
It makes sense that we define molar mass in terms of carbon because being element six it can
be thought of in terms of our regular hexagon which defines pi as an integer, the integer 3 (that
is to say as a whole number, 3 is not a fraction in that there is nothing but zeros after the
decimal). Carbon can be thought of in terms of the regular hexagon because it describes the
closest packing of equal radius spheres (a so-called “six-around-one”):!
But though carbon may be six protons, it has six neutrons giving it
a molar mass of 12.01 approximately twice it atomic number of
six. But twelve is our dodecagon which inscribes silicon if it is to
line up with carbon as the regular octagon. And here it is
interesting to note that carbon is made in stars by combining
beryllium-8 with helium, the eight of our regular octagon.!
Silicon is below carbon in group 14 and below that is germanium. Germanium is the other
primary semiconductor element used in transistor technology. In fact it was the first one used
and is called the first generation semiconductor where silicon is called a second generation
semiconductor and is what we mostly use today. Germanium is element 32 and has a molar
mass of 72.64. We have 72.64-32=40.64 giving it 40 neutrons. In considering the weighted
average of germanium most atoms have 42 neutrons (germanium-74). Ge consists of 5
isotopes:!
a =
s/2
tan(θ /2)
=
0.5
tan(15
∘
)
= 1.866
Si
C
=
0.118
0.077
= 1.532
a
Si
a
C
=
1.866
1.2071
= 1.54585
1.532
1.54585
100 = 99
of 18 32
!
The electronic configuration of germanium is and has a radius of
0.137nm and a Vander Walls radius of 0.211nm. We can predict the atomic numbers of carbon,
silicon, germanium, tin…as we move down group 14 with mathematical patterns combined
with logical statements:!
If n<2!
{!
(n=1,2,3,….)!
!
If n>1; i<3!
{!
(n=2, 3. 4….). (i=1, 2, 3,…)!
!
!
For!
{!
(n=2,3,4,…)!
!
(Ar)(3d )
10
(4s)
2
(4p)
2
Z = 2
n
+ 2
n+1
Z = 2
1
+ 2
2
= 2 + 4 = 6 = carbon
Z = i ⋅ 2
n
+ 2
n+1
Z = 1 ⋅ 2
2
+ 2
3
= 4 + 8 = 12 = silicon
Z = 2 ⋅ 2
3
+ 2
4
= 2 ⋅ 8 + 16 = 16 + 16 = 32 = ger m anium
Z = n(3
n
+ 2
n+2
)
Z = 2(3
2
+ 2
4
) = (9 + 16) = 50 = t in
of 19 32
If carbon is octagon (8), silicon dodecagon (12) then germanium is 16-gon. We have…!
!
!
a=2.513669746. !
!
!
a=2.513669646, Ge=0.137nm!
If a1 is octagon a1=1.2071 and a2 is 2.51367 (16-gon) then…!
!
Which is approximately chlorine (Cl=35.45g/mol). If a1 is octagon a1=1.2071 and a2 is
dodecagon a2=1.866 then…!
!
Which is approximately titanium Ti=47.88 then if we average these we have!
!
This is approximately the atomic number of calcium (Ca=40.08 g/mol). Calcium is the primary
component of the mineral component of bone, hydroxyapatite (HA). It does indeed have a
connection to germanium and silicon the primary components of AI circuitry. If we look at the
data for HA, Si, and Ge in terms of density we have!
Density of silicon is Si=2.33 grams per cubic centimeter.
Density of germanium is Ge=5.323 grams per cubic centimeter.
Density of hydroxyapatite is HA=3.00 grams per cubic centimeter.
This is
a =
(s/2)
tan(θ/2)
=
0.5
tan(11.25
∘
)
360
16
= 22.5
22.5
2
= 11.25
a
2
= 6.318535592
a
2
+ (s /2)
2
= 2.62915448
D = 5.125830895
P/D = 3.121445152 ≈ π
Ge
x
=
a
2
a
1
x = 72.64
1.2071
2.51367
= 34.88275868g/m ol
x = 72.64
1.2071
1.866
= 46.99021651 ≈ 47g/mol
34.88275868 + 46.99021651
2
= 40.9364876 ≈ = 41g /mol
of 20 32
where
Where HA is the mineral component of bone, Si is an AI semiconductor material and Ge is an AI
semiconductor material. This means
The harmonic mean between Si and Ge is HA,…
This is the sextic,…
Which has a solution
Where x=Si, and y=Ge. It works for density and molar mass. It can be solved with the online Wolfram
Alpha computational engine. But,…
3
4
Si +
1
4
G e ≈ H A
H A = Ca
5
(PO
4
)
3
OH
Si
H A
Si +
[
1 −
Si
H A
]
G e = H A
2 SiG e
Si + G e
≈ H A
x
2
(x + y)
4
− x y(x + y)
4
+ 2x y
2
(x + y)
3
− 4x
2
y
2
(x + y)
2
= 0
Si
G e
=
1
2 + 1
Si ≈ G e − H A
H A ≈
2 SiG e
Si + G e
Si ≈ G e −
2 SiG e
Si + G e
(Si + G e)G e
Si + G e
−
(Si + G e)Si
Si + G e
−
2 SiG e
Si + G e
= 0
G e
2
− 2SiG e − Si
2
Si + G e
= 0
x
2
− 2x y − y
2
= 0
x
2
− 2x y = y
2
x
2
− 2x y + y
2
= 2y
2
(x − y)
2
= 2y
2
x − y =
±
2y
of 21 32
And we find this is even more accurate by molar mass:
93% accuracy
We actually find
Si/Ge=
98.78% accuracy
The mineral component of bone hydroxyapatite (HA) is
The organic component of bone is collagen which is
We have
x = y + 2y
x = y(1 + 2)
x
y
= 1 + 2
y
x
=
1
2 + 1
Si
G e
≈
1
2 + 1
Si
G e
=
28.085
72.64
= 0.386632709
1
2 + 1
= 0.4142
0.386632709 ≈ 1 − ϕ = 0.381966011
Ca
5
(PO
4
)
3
OH = 502.32
g
m ol
C
57
H
91
N
19
O
16
= 1298.67
g
m ol
Ca
5
(PO
4
)
3
OH
C
57
H
91
N
19
O
16
= 0.386795722
ϕ = 0.618033989
1 − ϕ = 0.381966011
of 22 32
98.75% accuracy
Si/Ge~
An accuracy of 99.95863%
They are almost exactly the same!
10. Silicon and Carbon
We guess that artificial intelligence (AI) has the golden ratio, or its conjugate in its means
geometric, harmonic, and arithmetic by molar mass by taking these means between doping
agents phosphorus (P) and boron (B) divided by semiconductor material silicon (Si) :
Which can be written
We see that the biological elements, H, N, C, O compared to the AI elements P, B, Si is the
golden ratio conjugate (phi) as well:
So we can now establish the connection between artificial intelligence and biological life:
Ca
5
(PO
4
)
3
OH
C
57
H
91
N
19
O
16
≈ (1 − ϕ)
Ca
5
(PO
4
)
3
OH
C
57
H
91
N
19
O
16
≈ (1 − ϕ)
PB
Si
=
(30.97)(10.81)
28.09
= 0.65
2 PB
P + B
1
Si
=
2(30.97)(10.81)
30.97 + 10.81
1
28.09
= 0.57
0.65 + 0.57
2
= 0.61 ≈ ϕ
PB(P + B) + 2PB
2(P + B)Si
≈ ϕ
C + N + O + H
P + B + Si
≈ ϕ
(P + B + Si )
PB(P + B) + 2PB
2(P + B)Si
≈ (C + N + O + H )
of 23 32
Which can be written:
Where HNCO is isocyanic acid, the most basic organic compound. We write in the arithmetic
mean:
Which is nice because we can write in the second first generation semiconductor as well
(germanium) and the doping agents gallium (Ga) and arsenic (As):
Where
Where ZnSe is zinc selenide, an intrinsic semiconductor used in AI, meaning it doesn’t require
doping agents. We now have:
11. Germanium And Carbon
We could begin with semiconductor germanium (Ge) and doping agents gallium (Ga) and
Phosphorus (P) and we get a similar equation:
,
In grams per mole. Then we compare these molar masses to the molar masses of the
semiconductor material Ge:
PB
[
P
Si
+
B
Si
+ 1
]
+
2 PB
P + B
[
P
Si
+
B
Si
+ 1
]
≈ 2HCNO
[
PB +
2 PB
P + B
+
P + B
2
][
P
Si
+
B
Si
+ 1
]
≈ 3HN CO
[
PB +
2 PB
P + B
+
P + B
2
][
P
Si
+
B
Si
+ 1
]
≈ HN CO
[
Ga
Ge
+
As
Ge
+ 1
]
Zn
Se
≈
[
P
Si
+
B
Si
+ 1
]
[
Ga
Ge
+
As
Ge
+ 1
]
PB
(
Zn
Se
)
+
2 PB
P + B
(
Zn
Se
)
+
P + B
2
(
Zn
Se
)
≈ HN CO
2Ga P
Ga + P
= 42.866
Ga P = 46.46749
2Ga P
Ga + P
1
Ge
=
42.866
72.61
= 0.59
of 24 32
Then, take the arithmetic mean between these:
We then notice this is about the golden ratio conjugate, , which is the inverse of the golden
ratio, . . Thus, we have
1.
2.
This is considering the elements of artificial intelligence (AI) Ga, P, Ge, Si. Since we want to find
the connection of artificial intelligence to biological life, we compare these to the biological
elements most abundant by mass carbon (C), hydrogen (H), nitrogen (N), oxygen (O),
phosphorus (P), sulfur (S). We write these CHNOPS (C+H+N+O+P+S) and find:
A similar thing can be done with germanium, Ge, and gallium, Ga, and arsenic, As, this time
using CHNOPS the most abundant biological elements by mass:
Ga P
1
Ge
=
46.46749
72.61
= 0.64
0.59 + 0.64
2
= 0.615
ϕ
Φ
ϕ ≈
1
Φ
Ga P(G a + P) + 2G a P
2(Ga + P)Ge
≈ ϕ
Ga P(G a + P) + 2G a P
2(Ga + P)Si
≈ Φ
CHNOPS
Ga + As + Ge
≈
1
2
[
Ga As +
2Ga As
Ga + As
+
Ga + As
2
][
Ga
Ge
+
As
Ge
+ 1
]
≈ CHNOPS
[
Ga
Si
+
As
Si
+ 1
]
Ga As
(
O
S
)
+
2Ga As
Ga + As
(
O
S
)
+
Ga + As
2
(
O
S
)
≈ CHNOPS
O
S
≈
[
Ga
Ge
+
As
Ge
+ 1
]
[
Ga
Si
+
As
Si
+ 1
]
Ga As(Ga + As) + 2G a As
2(Ga + As)Ge
≈ 1
of 25 32
We can also make a construct for silicon doped with gallium and phosphorus:
And for germanium doped with gallium and phosphorus:
The Dynamic Construct
Above we see the artificial intelligence (AI) elements pulled out of the periodic table of the elements. As
you see we can make a 3 by 3 matrix of them and an AI periodic table. Silicon and germanium are in
group 14 meaning they have 4 valence electrons and want 4 for more to attain noble gas electron
C + H + N + O + P + S
Ga + As + Ge
≈
1
2
(C + N + O + H ) ≈
2(Ga + P)Si
Ga P(G a + P) + 2G a P
(P + B + Si )
HNCO ≈
2(Ga + P)Si
(Ga + P)
[
Ga P +
2GaP
Ga + P
]
(P + B + Si )
HNCO ≈
2(P + B + Si )Si
Ga P +
2GaP
Ga + P
Ga P(G a + P) + 2G a P
2(Ga + P)Ge
≈ ϕ
[
Ga P +
2Ga P
Ga + P
+
Ga + P
2
][
P
Ge
+
B
Ge
+
Si
Ge
]
≈ HN CO
[
Ga
Ge
+
As
Ge
+ 1
]
Ga P
(
B
S
)
+
2Ga P
Ga + P
(
B
S
)
+
Ga + P
2
(
B
S
)
≈ HN CO
of 26 32
configuration. If we dope Si with B from group 13 it gets three of the four electrons and thus has a
deficiency becoming positive type silicon and thus conducts. If we dope the Si with P from group 15 it
has an extra electron and thus conducts as well. If we join the two types of silicon we have a
semiconductor for making diodes and transistors from which we can make logic circuits for AI.
As you can see doping agents As and Ga are on either side of Ge, and doping agent P is to the right of Si
but doping agent B is not directly to the left, aluminum Al is. This becomes important. I call (As-Ga) the
differential across Ge, and (P-Al) the differential across Si and call Al a dummy in the differential because
boron B is actually used to make positive type silicon.
That the AI elements make a three by three matrix they can be organized with the letter E with subscripts
that tell what element it is and it properties, I have done this:
Thus E24 is in the second row and has 4 valence electrons making it silicon (Si), E14 is in the first row
and has 4 valence electrons making it carbon (C). I believe that the AI elements can be organized in a 3 by
3 matrix makes them pivotal to structure in the Universe because we live in three dimensional space so
the mechanics of the realm we experience are described by such a matrix, for example the cross product.
Hence this paper where I show AI and biological life are mathematical constructs and described in terms
of one another.
We see, if we include the two biological elements in the matrix (E14) and and (E15) which are carbon and
nitrogen respectively, there is every reason to proceed with this paper if the idea is to show not only are
the AI elements and biological elements mathematical constructs, they are described in terms of one
another. We see this because the first row is ( B, C, N) and these happen to be the only elements that are
not core AI elements in the matrix, except boron (B) which is out of place, and aluminum (Al) as we will
see if a dummy representative, makes for a mathematical construct, the harmonic mean. Which means we
have proved our case because the first row if we take the cross product between the second and third rows
are, its respective unit vectors for the components, meaning they describe them!
12. The Computation
E
13
E
14
E
15
E
23
E
24
E
25
E
33
E
34
E
35
A = (Al, Si, P )
B = (G a, G e, A s)
A ×
B =
B
C
N
Al Si P
G a G e As
= (Si ⋅ A s − P ⋅ G e)
B + (P ⋅ G a − Al ⋅ A s)
C + (Al ⋅ G e − Si ⋅ G a)
N
A ×
B = − 145
B + 138
C + 1.3924
N
A = 26.98
2
+ 28.09
2
+ 30.97
2
= 50g /m ol
of 27 32
And silicon (Si) is at the center of our AI periodic table of the elements. We see the biological elements C
and N being the unit vectors are multiplied by the AI elements, meaning they describe them! But we have
to ask; Why does the first row have boron in it which is not a core biological element, but is a core AI
element? The answer is that boron is the one AI element that is out of place, that is, aluminum is in its
place. But we see this has a dynamic function.
13. The Dynamic Function
The primary elements of artificial intelligence (AI) used to make diodes and transistors, silicon (Si) and
germanium (Ge) doped with boron (B) and phosphorus (P) or gallium (Ga) and arsenic (As) have an
asymmetry due to boron. Silicon and germanium are in group 14 like carbon (C) and as such have 4
valence electrons. Thus to have positive type silicon and germanium, they need doping agents from group
13 (three valence electrons) like boron and gallium, and to have negative type silicon and germanium they
need doping agents from group 15 like phosphorus and arsenic. But where gallium and arsenic are in the
same period as germanium, boron is in a different period than silicon (period 2) while phosphorus is not
(period 3). Thus aluminum (Al) is in boron’s place. This results in an interesting equation.
The differential across germanium crossed with silicon plus the differential across silicon crossed with
germanium normalized by the product between silicon and germanium is equal to the boron divided by
the average between the germanium and the silicon. The equation has nearly 100% accuracy (note: using
an older value for Ge here, is now 72.64 but that makes the equation have a higher accuracy):
=
0.213714502
2(10.81)/(72.64+28.085)=0.214643832
% accuracy
B = 69.72
2
+ 72.64
2
+ 74.92
2
= 126g /m ol
A ⋅
B = A Bcosθ
cosθ =
6241
6300
= 0.99
θ = 8
∘
A ×
B = A Bsinθ = (50)(126)sin8
∘
= 877.79
877.79 = 29.6g /m ol ≈ Si = 28.09g /m ol
Si(A s − G a) + G e(P − Al )
SiG e
=
2B
Ge + Si
(28.085)(74.9216 − 69.723) + 72.64(30.97376200 − 26.981539)
(28.085)(72.64)
0.213714502
0.214643832
= 99.567
of 28 32
Thus, due to an asymmetry in the periodic table of the elements due to boron we have the
harmonic mean between the semiconductor elements (by molar mass):
This is Stokes Theorem if we approximate the harmonic mean with the arithmetic mean:
We can make this into two integrals:
If in the equation (The accurate harmonic mean form):
We make the approximation
Then the Stokes form of the equation becomes
Thus we see for this approximation there are two integrals as well:
Si
B
(As − G a) +
Ge
B
(P − Al ) =
2SiG e
Si + G e
∫
S
( ∇ × u ) ⋅ d S =
∮
C
u ⋅ d r
∫
1
0
∫
1
0
[
Si
B
(As − Ga) +
Ge
B
(P − Al )
]
d x d y ≈
1
Ge − Si
∫
Ge
Si
x d x
∫
1
0
∫
1
0
Si
B
(As − Ga)d ydz ≈
1
3
1
(Ge − Si )
∫
Ge
Si
x d x
∫
1
0
∫
1
0
Ge
B
(P − Al )d x dz ≈
2
3
1
(Ge − Si )
∫
Ge
Si
yd y
Si
B
(As − Ga) +
Ge
B
(P − Al ) =
Ge − Si
Ge
Si
dx
x
2SiGe
Si + Ge
≈ G e − Si
∫
1
0
∫
1
0
[
Si
B
(As − Ga) +
Ge
B
(P − Al )
]
d yd z =
∫
Ge
Si
d x
of 29 32
14. Conclusion
We have
Where
Gold and Iron are the quintessential elements in that gold is the finest conductor at extreme temperatures,
has had the highest value as a metal for ceremonial crafts and representation of money, since ancient
times and iron has defined the Iron Age where metallurgy and tool making reached its height. Silicon,
germanium, copper, and gold are at the crux electrical and transistor technologies as well as phosphorus,
boron, gallium and arsenic. Their mathematical representations are here connected to the stars and open
up into three dimensional geometry in the form of Stokes theorem as five-fold symmetry. The biological
elements are mathematical constructs as well and describe them. Like the interval of a fifth, musically, it
is .
∫
1
0
∫
1
0
Si
B
(As − Ga)d ydz =
1
3
∫
Ge
Si
dz
∫
1
0
∫
1
0
Ge
B
(P − Al )d yd z =
2
3
∫
Ge
Si
dz
∫
1
0
∫
1
0
(
Si
B
(As − G a) +
Ge
B
(P − Al )
)
d yd z ≈
5
∫
Ge
Si
∫
Ge
Si
∇ ×
v ⋅ d
a
v = (−CP ⋅ y, SiGe ⋅ z, G a A s ⋅ y)
d
a =
(
zd yd z
i + yd yd z
k
)
5
5
∏
i=1
x
i
≈ Fe
5
Si ⋅ G e ⋅ C ⋅ Ag ⋅ Au ≈ Fe
L = M
Au
Fe
Φ
of 30 32
Appendix 1
Ge=72.64!
As=74.9216!
Si=28.085!
Ga=69.723!
C=12.011!
P=30.97376200!
=!
=!
!
!
!
!
!
=154,082,837.980+16,452,521.6822=!
!
=!
(28.085)(72.64)(12.085)(107.8682)(196.9657)=!
!
Where we have substituted carbon C=12.01 for copper Cu. We use Cu, Ag, Au because they
are the middle column of our electronics matrix, they are the finest conductors used for
(Ge ⋅ As − Si ⋅ G a)
i + (C ⋅ P)
k
[
(72.64)(74.9216) − (28.085)(69.723)
]
i +
[
(12.011)(30.97376200)
]
k
3,484.134569
(
g
mol
)
2
i + 372.025855
(
g
mol
)
2
k
∫
Ge
Si
∫
Ge
Si
(
3,484.134569
(
g
mol
)
2
i + 372.025855
(
g
mol
)
2
k
)
⋅
(
zdydz
i + yd ydz
k
)
∫
Ge
Si
∫
Ge
Si
(
3,484.134569
(
g
mol
)
2
⋅ zdzd y + 372.025855
(
g
mol
)
2
⋅ ydzd y
)
∫
Ge
Si
3,484.134569
(
(72.64 − 28.085)
2
2
)
dy +
∫
Ge
Si
372.025855y ⋅ (72.64 − 28.085)d y
3458261.42924
(
g
mol
)
4
(72.64 − 28.085) + 16575.6119695
(
g
mol
)
3
(
(72.64 − 28.085)
2
2
)
170,535,359.662
(
g
mol
)
5
5
∏
i=1
x
i
= Si ⋅ Ge ⋅ C ⋅ Ag ⋅ Au
523,818,646.5
g
5
mol
5
of 31 32
electrical wire. We use C, Si, Ge because they are the middle column of our AI Biomatrix. Si
and Ge are the primary semiconductor elements used in transistor technology (Artificial
Intelligence) and C is the core element of biological life. We have!
!
!
Perimeter/Diameter of regular hexagon = 3.00!
!
The same value as our 3.0716 if taken at two places after the decimal.!
523,818,646.5
170,535,359.662
= 3.0716
π = 3.141...
3.141 + 3.00
2
= 3.0705
of 32 32
The Author!
of 1 19
Asteroids/Meteors/Meteorites 01 02 03
Essays where anthropological cosmology
meet with cosmology in physics
Genesis Project California 2021!
⋅
⋅
of 2 19
© 2021 By Ian Beardsley"
ALL RIGHTS RESERVED INCLUDING THE RIGHT OF REPRODUCTION IN WHOLE OR IN
PART IN ANY FORM. PUBLISHED BY GENESIS PROJECT!
of 3 19
Abstract
It would seem the dinosaurs went extinct 65 million years ago because a meteor
impacted the Earth in the Yucatan. This kicked up a lot of dust into the atmosphere
blocking sunlight causing darkness and vegetation to die, only the small mammals were
very successful. It would seem this gave way for humans to evolve from mammals
instead of becoming reptilian. In this sense we might guess much intelligent life in the
universe could be of a Reptilian Nature, if the process by which life happens is Universal.
Can we understand our origins by looking at small rocks that burn-up and make it to the
Earth surface, that originated in the asteroid belt, a place where matter was torn apart
into anything from small pebbles to, meter-wide rocks, to several miles in diameter,
because of its distance from the sun and the spacing of the planets acting on them?
Incredible enough this vast region of small rocks, and large iron-nickel boulders is shown
here to be so deeply connected with the physical constants that arise from the Nature of
the relationships between mass, length, and time in our Universe, that as unfathomable
as it would seem, with these small rocks found on earth we can arrive at some
remarkably accurate results. There is a big mystery surrounding life and it seems to be
connected to the meteors.
Asteroids/Meteors/Meteorites 01"
I had found (Beardsley Essays In Cosmic Archaeology. 2021) where I suggested the idea of
proton seconds, that is six protons-seconds, which is carbon the core element of biological life
if we can figure out a reason to divide out the seconds. I found"
Equation 1. "
Where h is Planck’s constant 6.62607E—34 Js, r_p is the radius of a proton 0.833E-15m, G is
the universal constant of gravitation 6.67408E-11 (Nm2)/(kg2), and c is the speed of light
299,792,459 m/s. And t_1 is t=1 second. is the Sommerfeld constant (or fine structure
constant) is 1/137. The mass of a proton is ."
The fine structure constant squared is the ratio of the potential energy of an electron in the first
circular orbit to the energy given by the mass of an electron in the Bohr model times the speed
of light squared: "
"
Alpha decay is the decay of elements where a helium nucleus is ejected from an element (alpha
particles). This happens with atoms heavier than nickel because the atom has to be heavy
enough that the internal repulsion between protons is high enough that the binding force has
trouble holding them together. However, interestingly beryllium-8 is an exception; it is much
lighter than nickel. Beryllium-8 was determined by Fred Hoyle to make carbon in nuclear
synthesis in stars by combining with helium. He sought to find the process by which carbon is
created because the Universe needs to make it if we are to have life as we know it. "
1
t
1
α
2
m
p
h4π r
2
p
Gc
= 6protons
α
m
p
= 1.67262E − 27kg
α
2
=
U
e
m
e
c
2
of 4 19
Alpha particles (helium nuclei) have a typical kinetic energy of 5MeV and a speed of 15,000,000
m/s. This is 1.6E-12 Joules and 1.5E7 m/s. Note the defining point here is nickel. This
becomes important because most meteors and asteroids are iron-nickel."
"
This is 1.5E7 meters"
"
The Solar mass is "
"
"
The Earth radius is 6,378km"
"
We have ( )"
"
About 40 pounds. A meteor has to have a size of at least 1 meter in diameter so as not burn up
completely before making it to the ground. That is, the size required for a meteor to become a
meteorite. About 3.3 feet in diameter. By the time it makes it to the ground it is 128-256 grams.
For stony irons, that is a density of 4 g/cm3 which is 4000 kg/m3 by these figures. The average
density of a so-called asteroidal chondritic meteor is 4200 kg/m3. Thus we have:"
"
We have 128 grams is 0.128kg in the lower limit for a meteorite. If we want to temper the
meteorite with the meteor before it burns up in the lower limit for size by using the geometric
mean we have multiplying both sides by two for second planet Venus:"
"
Using an exact value for the mass of the sun:"
1.5E 7
m
s
⋅ (1secon d ) = x
1.6E − 12N ⋅ m
1.5E 7m
= 1.0667E − 19N ≈ 1E − 19Newton s
M
⊙
= 1.989E 30kg ≈ 2E 30kg
1E − 19kg
m
s
2
⋅
1
2E 30kg
= 5E − 50
m
s
2
M =
ar
2
G
M =
(5E − 50m /s
2
)(6,378,000m)
2
6.67432E − 11
= 3.0E − 26kg
m
p
= 1.67262E − 27kg
M
m
p
= 18.22kg
4
3
π(0.5m)
3
⋅ 4200
kg
m
3
= 2,100kg
4,200 ⋅ 0.17357kg = 27kg
of 5 19
"
"
This is Venus orbit in astronomical units, which is Venus orbit divided by Earth orbit. Venus is
said to be a failed Earth in that she underwent a runaway greenhouse effect. The chondritic
meteoroid is a meteor that came from the asteroid belt. We currently study the asteroid belt to
catalog asteroid orbits to see if any might be on a trajectory to collide with earth, so we can
knock it off such a trajectory and not suffer the fate of the dinosaurs whose extinction was
brought about by such an asteroid landing in the Yucatan. What this amount to is:"
Equation 2. "
Where E_alpha is the energy of an alpha particle, and v_alpha its velocity. R_e is the radius of
the Earth. And,…"
Equation 3. "
Where the c subscript denotes chondritic meteors. Combining equations 1, 2, and 3 we have"
Equation 4. "
In work of mine (Essays In Cosmic Archaeology Volume Four, 2021) I explained the relationship
between planetary orbits and the primary semiconductor elements silicon (Si) and germanium
(Ge) with the very accurate result (silicon also being the main component of sand)."
Equation 5. "
By molar mass. This gives"
Equation 6: "
See Appendix one for this first section of Asteroids/Meteors/Meteorites for the calculations. "
M
m
p
= 19.54kg
19.54kg
27kg
= 0.72
E
α
v
α
t
1
⋅
1
M
⊙
R
2
e
G
⋅
1
m
p
= 19.54kg/s
4R
3
c
M
m
⋅ ρ
c
= 27kg
E
α
v
α
1
t
1
R
E
2
M
⊙
1
Gm
p
4R
3
c
ρ
c
M
m
=
19.54
27
= 0.72
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
= 0.72
E
α
v
α
1
t
1
R
E
2
M
⊙
1
Gm
p
4R
3
c
ρ
c
M
m
=
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
of 6 19
Discussion: It would seem these small rocks that must be at least a meter in diameter
(meteors) to make it to the earth without burning up, and that we can find on the surface
on the average 0.128 kg to 0.256 kg can allow us to probe into some deep questions:
Does life evolve by a common process throughout the universe (We we see the meteors
are described by 6 proton-seconds and 6 protons is carbon, the core element of life on
earth)? Was Earth hit by a large meteor several miles across so the Dinosaurs would go
extinct giving way to mammalian, upright life with an opposable thumb to evolve into
existence? Or, are we a chance fluke? Or, does this happen on other planets evolving
throughout the universe quite often? Is there intelligent reptilian life throughout the
universe and if so how much would be reptilian and how much mammalian. If not, why
did the dinosaurs come into existence if whatever was responsible for life on earth was
to make our solar system such that an asteroid would bring about their extinction. Are
there intelligent life forms other than reptilian and mammalian throughout the universe,
or that is not based on carbon? As we shall see, while we cannot answer these
questions, we can however, develop further causes in asteroids/meteors/meteorites 02.
Interestingly t=t1=1 seconds are used in both equation 1 and equation 4 connecting
carbon the core element of life to the meteors.
Asteroids/Meteors/Meteorites 02"
If we can get down to this kind of accuracy for Venus orbit using earth size, the mass of the
sun, the lowest energy orbit in the Bohr atom (fine structure constant) through the lower limit of
a meteor to make it to earth surface (become a meteorite) for these small rocks in the asteroid
belt using proton-seconds like this, the proton-seconds might be useful for modeling the solar
system, which has so many complex unmanageable amounts of factors. In essence these
equations outline an approach. Might even be able to use the Schrödinger wave-equation with
these small rocks in the asteroid belt to determine the probability of asteroids being in the earth
region of space at a given time. "
We have the Schrödinger wave equation is
We must solve it for psi and find psi squared.. "
"
Which is "
"
Because psi is a complex function, so we must multiply it with its complex conjugate and take
the absolute value. To find psi for a region around the earth between the distance from the
earth to the moon all the way around the sun; Near earth objects (NEO’s) are classified by such
a region around the earth, would be very difficult to do for the meteors in the asteroid belt a
meter in diameter as used in my calculations considering them as very small quanta
comprising a cloud like electron clouds in an atom, compared to the size of planets, moons,
and asteroids. However there may be another avenue. We have a data estimate. "
iℏ
∂ψ
∂t
=
(
ℏ ∇
2
2 m
+ V( r )
)
ψ ( r, t)
ψ (x, y, z)
2
d x d ydz
ψ
2
= [ψ (x, y, z, y)][ψ*(x, y . z, t)]
of 7 19
The Earth is hit by about 6,100 meteors a year that are large enough to make it to the ground,
which is about 17 everyday according to Gonzalo Tancredi an astronomer at the University of
the Republic in Montevideo, Uruguay. He arrived at this from a database that says that in the
last 95 years 95 people have observed the rare event where a large meteor the size of a
minivan have entered the atmosphere and broke up into small rocks that showered the sky,
many of them landing on rooftops, which is about 8 per year. To arrive at his figure of 6,100 he
reasoned that people only inhabit 0.44% of the Earth’s land area which is 0.13% of it surface
area and therefore for every observed impact another 770 that impact the Earth go
unobserved. "
Thus 6,100 meteors a year is a frequency of (6100)/(365 days)(24 hrs)(60 min)(60 sec)=(6100)/
(31536000 seconds per year). This is a frequency of 0.0002 meteors per second. "
"
Is the frequency we can use in plank’s equation%
"
I first estimated our asteroid of radius (0.5 m) to be 2,200 kg. Which gave"
"
The average orbital velocity of an asteroid in the asteroid belt is about 40km per second. Thus
for a Planck constant for sizes on the order of meteors we suggest there exists some distance
between the asteroid belt at its outer edge at 3.2AU and the outer reaches of the solar system
at Pluto average orbit of 39.5AU. We arrive at it by taking the geometric mean between these
two distances (foot note 1):
"
1
"
This corresponds to an orbital velocity of"
"
"
The rotational kinetic energy of the Earth is"
ν = (2E − 4) ⋅ s
−1
1
2
mv
2
= E = hυ
h =
1,100
0.0002
v
2
(3.2)(39.5) = 22AU
v
2
=
GM
⊙
3.31868E15m
= 40,000m
2
/s
2
h = 5,500,000(40,000) = 2.2E11J ⋅ s
What I mean by this is 39.5-22=17.5 and 17.5+3.2 is approximately 22 where 3.2 is the
1
asteroid belt. This is further interesting in that this reconciles the harmonic mean with
arithmetic mean for Mars orbit which is 1.5. The harmonic mean is 2(39.5)(22)/(39.5+22)=28.26.
28.26-3.2=25 and (22+25)/2=23.5. And, 23.5-1.5=22. The asteroid belt is the first orbit after
Mars.
of 8 19
"
Which is 2.138E29J. This corresponds to an upsilon of"
"
This is the frequency of X-rays which have a wavelength of"
"
This corresponds to the kinetic energy of an electron using it as the de Broglie wavelength of"
"
This interesting in light of the Richardson Effect. Electrons can be emitted from metals. This is
modeled by considering them in some kind of a potential well created by the ions which
depends on the structure of the metal. The modeling can be done such that the potential of the
electron moving in the metal is a constant -W until it reaches the surface at which point W is
zero and any electron here whose kinetic energy due to its motion if perpendicular to the
surface is greater than the barrier potential W will escape. Emission of electrons from a metal
occurs at high temperatures resulting in this effect called the thermionic effect or photoelectric
effect. Thermionic emission (The Richardson Effect) ."
But the interesting thing is we don’t have to calculate W, but can determine it experi- mentally
by looking at the refractive index of a metal for de Broglie waves associated with an electron
beam hitting the metal whose initial kinetic energy is E. The refractive index is"
"
Measuring diffraction values for different values of E we can derive W. Davisson and Germer in
1927 derived that and found for Tungsten W should be 13.5eV but measurements show it is =
4.5eV . But the quantum statistical formula works because the depth of the quantum well W
minus the fermi energy ✏
F
= 9eV for tungsten is 13.5-9=4.5eV. In the case of nickel (Ni) the
experimental result is 5.0eV and the theoretical result for the Fermi level is 11.8eV gives
potential well depth W of 16.8 eV. Experimental diffraction of electrons on nickel result in (17
+/- 1) eV. This is our energy from the de Broglie wavelength that corresponds to our Planck
constant for the material in the asteroid belt. "
"
Most meteors are iron-nickel meteors.!
K =
1
2
Iω
2
υ = E /h = 2.138E 29J/2.2E11Js = 9.72E17s
−1
λ =
299792458m /s
9.72E17s
−
1
= 3E − 10 = 0.3n m
K =
h
2
2m λ
2
= 16.8eV
n =
λ
in
λ
out
=
(
E + W
E
)
1/2
K =
h
2
2m λ
2
= 16.8eV
of 9 19
Asteroids/Meteors/Meteorites 03"
Concerning equation 5:"
"
Why are the meteors connected to silicon equation 6:"
"
Through venus. Silicon actually appears in many meteors as (silicates). The types of meteors
are:"
There are three types of meteorites: 1. Iron meteorites%
2. Stony- iron meteorites%
3. Stony meteorites "
The Iron meteorites are mostly Iron-nickel metal with small amounts of sulphide and carbide
minerals. This is the element nickel (Ni) so prominent in our calculations. Meteors seem to have
a similar structure to the terrestrial planets Mercury, Venus, Earth, and Mars in that they have
an iron core and concentric layers surrounded by a silicate mantle and crust. Thus meteorites
are studied to tell us about how the terrestrial planets might have formed. If we look at stars on
the main sequence we find their luminosity is given by: "
"
Where L is the luminosity of a star in solar luminosities and M is its mass in solar masses. I find
it interesting that in molar mass 3.5=Au/Fe where Au is gold=196.96 g/mol and Fe is iron=55.85
g/mol. Thus we have "
"
We consider the protoplanetary disc from which the planets formed. First we form a table of
the masses of the planets."
"
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
= 0.72
E
α
v
α
1
t
1
R
E
2
M
⊙
1
Gm
p
4R
3
c
ρ
c
M
m
=
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
L = M
3.5
L = M
Au/Fe
of 10 19
"
Taking the protoplanetary disc as a thin disc we integrate from its center to the edge, with
density decreasing linearly to zero at the edge. Thus, if the density function is given by"
"
And, our integral is"
"
Si + Ge
2
=
2.33 + 5.323
2
= 3.8265g/cm
3
ρ(r) = ρ
0
(
1 −
r
R
)
M =
∫
2π
0
∫
R
0
ρ
0
(
1 −
r
R
)
rdrdθ
of 11 19
"
"
The mass of the solar system adding up all the planets yields"
"
That accounts for"
82% of the mass of the solar system not including the sun, that is, of the
protoplanetary disc surrounding the sun."
Using germanium alone, we get,"
"
If we weight the mixture of silicon and germanium as 1/3 and 2/3, then we have"
"
Which is very close."
93%"
This is all very good, because I only used the planets and asteroids."
Weighting silicon and germanium as 1/4 and 3/4 we have"
"
Which accounts for"
98%"
Of the mass of the solar system (very accurate)."
This mixture of 1/4 to 3/4 is a combination that exists in the Earth atmosphere which is
approximately the mixture of oxygen to nitrogen. The earth atmosphere can be considered a
mixture of chiefly O2 and N2 in these proportions:"
M =
πρ
0
R
2
3
π(3.8265)(7.4 × 10
14
)
2
3
= 2.194 × 10
30
gra ms
M = 2.668 × 10
30
gra ms
2.194
2.668
100 =
π(5.323)(7.4 × 10
14
)
2
3
= 3.05 × 10
30
gra ms
π(4.32467)(7.4 × 10
14
)
2
3
= 2.48 × 10
30
gra ms
2.48
2.668
100 =
π(4.4 . 57475)(7.4 × 10
14
)
2
3
= 2.623 × 10
30
gra ms
2.623
2.668
100 =
of 12 19
Air is about 25% oxygen gas (O2) by volume and 75% nitrogen gas (N2) by volume meaning
the molar mass of air as a mixture is:"
"
By molar mass the ratio of air to H20 (water) is about the golden ratio:"
"
I am not saying the solar system was a thin disk with density of the weighted mean somewhere
between silicon and germanium, but that it can be modeled as such, though if the
protoplanetary disk that eclipses epsilon aurigae every 27 years is any indication of what a
protoplanetary cloud is like, it is a thin disk in the sense that it is about 1 AU thick and 10 AU in
diameter. This around a star orbiting another star."
But further why not consider the value t1=1 second that connects the carbon of life to the
meteors?"
The second does have meaning especially in connection with life. By dividing the day into 24
hours, the hour into 60 minutes, and the minute into 60 seconds, the second is 1/86400 of day.
By doing this we have a twelve-hour daytime at spring and fall equinox on the equator, 12
being the most divisible number for its size (smallest abundant number). That is to say that
twelve is evenly divisible by 1,2,3,4,6 which precede it and 1+2+3+4+6=16 is greater than
twelve. As such there is about one moon per 30 days and about 12 moons per year (per each
orbit) giving us a twelve-month calendar. This is all further convenient in that the moon and
earth are in very close to circular orbits and the circle is evenly divisible by 30, 45, 60, and 120
if we divide the circle into 360 degrees which are special angles very useful to the workings of
physics and geometry. Further, the 360 degrees of a circle are about the 365 days of a year
(period of one earth orbit) so as such the earth moves through about a degree a day in its
journey around the sun. Thus, through these observations down through the ages since ancient
times we have constructed the duration of a second wisely enough to make a lot work
together. Now we see 6 protons, which is carbon the core element of biological life on the
planet where all of this came together is deeply connected with the second that defines it all. !
0.25O
2
+ 0.75N
2
≈ air
air
H
2
O
≈ Φ
of 13 19
Appendix 1!
of 14 19
!
of 15 19
!
of 16 19
!
of 17 19
!
of 18 19
!
of 19 19
"
Author: Ian Beardsley"
of 1 20
Extant Numerology
Ian Beardsley (Oct 20, 2021)!
Physics, University of Oregon
Genesis Project California 2021
⋅
⋅
of 2 20
When doing research certain patterns sometimes show up as a result of the units we use. This
might suggest the units we use have meaning. In a sense they do. I wrote (Beardsley, Essays in
Cosmic Archaeology Volume 2, 2021):!
We only need to explain the significance of the duration of one second. The second does
have meaning especially in connection with life. By dividing the day into 24 hours, the
hour into 60 minutes, and the minute into 60 seconds, the second is 1/86400 of day. By
doing this we have a twelve-hour daytime at spring and fall equinox on the equator, 12
being the most divisible number for its size (smallest abundant number). That is to say that
twelve is evenly divisible by 1,2,3,4,6 which precede it and 1+2+3+4+6=16 is greater than
twelve. As such there is about one moon per 30 days and about 12 moons per year (per
each orbit) giving us a twelve-month calendar. This is all further convenient in that the
moon and earth are in very close to circular orbits and the circle is evenly divisible by 30,
45, 60, and 120 if we divide the circle into 360 degrees which are special angles very
useful to the workings of physics and geometry. Further, the 360 degrees of a circle are
about the 365 days of a year (period of one earth orbit) so as such the earth moves
through about a degree a day in its journey around the sun. Thus, through these
observations down through the ages since ancient times we have constructed the
duration of a second wisely enough to make a lot work together. Now we see 6 protons
and 6 neutrons, which is carbon the core element of biological life on the planet where all
of this came together is deeply connected with the second that defines it all.
I also wrote (Beardsley, Weird Mathematics, 2021)!
We have to ask first, what is a gram? A thousand grams (a kilogram) is the mass of a cube of
1/10 of a meter on each side. And what is a meter? It was originally one ten millionths of the
distance from the North Pole to the equator, and is still close to that. This is the metric system.
It is based on ten. But why? Because we have a base ten counting system; we start with one,
then proceed to 2, then to 3…until we we get to 10 and start over…one zero is ten, one one is
eleven, one two is thirteen, and so on. Many have asked why we have a base ten counting
system and no one knows why, but it is thought to be because we have ten fingers to count on.
Then, we ask, what is a mole? It is a number used in chemistry because atoms, molecules and
compounds occur in large numbers and a dozen just won’t do. Therefore it is a very large
number. But how did we define it? Well carbon is at the core of life and 12 is the most divisible
number for its size in that it is divisible by 1, 2, 3, 4, 6,…evenly. And 1+2+3+4+6=16 is greater
than 12 which makes it the smallest abundant number. For instance four is divisible evenly by
one and two, but one plus two equals 3 which is less than four. Thus, we said carbon has
twelve grams per mole. This allowed us to determine the mole as the number of atoms in 12
grams of carbon, grams defined in terms of water and the earth’s size, The number was
determined by Avagadro and is 6.02E23.
This is best explained by something done by the astronomer Christian Huygens. He noted if pi
squared is 9.87 and we use this as earth acceleration instead of 9.81, then for the period of a
pendulum:
T = 2π
l
g
of 3 20
We have
If l=1 meter then T=2 seconds, one swing to the right is one second. He suggested we define
the meter such that the period is 2 seconds if we use it for l.
I found consecutive integers in gallium and arsenic when taken to two places after the decimal.
(Beardsley, Mathematical Construct in Nature, 2021):
We see the eccentricity is
Which is 9 figures eight of which are the first eight consecutive integers 1,2,3,4,5,6,7,8. The
only number that occurs twice is 2. Kind of interesting.
T = 2
π
2
l
g
= 2 l
1 −
Ga
As
= 1 −
69.72
74.92
= 0.263452781
of 4 20
The Search
We are interested in blocks of elements in the periodic table that can be taken directly out of
the periodic table as 3 by 3 matrices so we can take the cross product with the top row of
elements describing the other two vectors as unit vectors. However, while we can do this with
scandium Sc, Titanium Ti, and vanadium V as aerospace metals describing the two rows below
them the groups 3 to 5, we cannot do this with agricultural elements which seem to be in two
separate 2 by 2 matrices:!
=(22.9897693)(40.08)-(24.305)(39.0983)!
=-28.854 g/mol squared!
The Secondary Nutrients (Mg, Ca, K) and,…!
=(12.011)(30.97376200)-(14.007)(28.085)!
=-21.3607 g/mol squared!
The primary nutrients (N, P)!
g/mol!
g/mol!
(5.372592+4.621768)/2=4.9968~5.00 g/mol=(H+He)=1.01+4.00!
If we consider what I will call the aerospace matrix:!
=!
A=(88.91, 91.22, 92.91)=157.6653!
B=(138.91, 178.49, 180.95)=289.65077!
!
=0.9951!
!
!
(
Na Mg
K Ca
)
(
C N
Si P
)
28.854 = 5.371592
21.3607 = 4.621768
Sc Ti V
Y Zr Nb
L a H f Ta
A Bcosθ = A ⋅ B
cosθ = 45,444.4104000/45,667.8755
θ = 5.67
∘
A Bsinθ = 4,512
of 5 20
!
Is between Zn and Ga: (Zn+Ga)/2=(65.39+69.72)/2=67.555 g/mol!
{(91.22)(180.9475)-(92.90637)((178.49)}Sc+{(92.90637)(138.9055)-(88.9084)(180.9475)}Ti!
+{(88.9084)(178.4866)-(91.22)(138.9055)}V=!
(-76.827)Sc+(3,182.547)Ti+(3,197.9983)V!
Which conveniently puts Sc, Ti, and V in the top row as unit vectors. Convenient because they
are aerospace metals as they are light and strong in that scandium, and titanium make light
strong alloys for jet engines and spacecraft, vanadium very rare used as a specialty alloy.!
I already did what I call the electronics matrix and the AiBiomatrix (Beardsley, The
Quintessential Elements 2021) which was the inspiration for this paper because of much
success with it, I had for the electronics matrix:!
=!
A=(106.42, 107.87, 65.39)=165.036!
B=(195.08, 196.97, 200.59)=342.18!
!
!
!
!
Is between Ag and Cd: (Ag+Cd)/2=(107.87+112.41)/2=110.14 g/mol which is down one and to
the left from our (Zn+Ga)/2. That is they are part of a diagonal.!
With Cu, Ag, and Au the malleable, ductile conductors most used for electrical wire. Which I
see now could more aptly be called the metallurgy matrix. The AiBiomatrix was!
!
!
4512 = 67.17g/mol
Ni Cu Z n
Pd Ag Cd
Pt Au Hg
56,472.0cosθ = 55,124.1476
θ = 12.5432
∘
A Bsinθ = 12,264.348
12,264.348 = 110.74g/mol
A ×
B =
B
C
N
Al Si P
Ga Ge As
= (Si ⋅ As − P ⋅ Ge)
B + (P ⋅ G a − Al ⋅ As)
C + (Al ⋅ Ge − Si ⋅ G a)
N
A ×
B = − 145
B + 138
C + 1.3924
N
of 6 20
With the middle column carbon the core of biological life, and Si, and Ge the primary
semiconductor elements used in transistor technology. We have!
!
!
!
!
!
!
!
!
!
Is half way between nitrogen and oxygen is (N+O)/2=(14.01+16.00)/2=15.005!
The Result
=15.163 g/mol!
=67.17 g/mol!
=110.74 g/mol!
15.163+67.17+110.74=193.073 g/mol=(Ir+Pt)/2=(192.22+195.08)/2=193.65g/mol!
A ×
B =
B
C
N
Al Si P
Ga Ge As
= (Si ⋅ As − P ⋅ Ge)
B + (P ⋅ G a − Al ⋅ As)
C + (Al ⋅ Ge − Si ⋅ G a)
N
A ×
B = − 145
B + 138
C + 1.3924
N
A = 26.98
2
+ 28.09
2
+ 30.97
2
= 49.76g /mol
B = 69.72
2
+ 72.64
2
+ 74.92
2
= 125.5g/m ol
A ⋅
B = A Bcosθ
cosθ =
6240.652
6244.88
= 0.999322965
θ = 2.11
∘
A ×
B = A Bsinθ = (49.76)(125.5)sin8
∘
= 229.924765
229.924765 = 15.163g/mol
B
C
N
Al Si P
Ga Ge As
Sc Ti V
Y Zr Nb
L a H f Ta
Ni Cu Z n
Pd Ag Cd
Pt Au Hg
of 7 20
Is between iridium and platinum. We take the ratio between our determinants, the agricultural
matrices and multiply them by this:!
!
!
(4.621768/5.371592)(193.65)=166.618271306 g/mol!
Where the decimal is 618 271 306!
And , , !
6/3=2 = diameter of a unit regular hexagon. Its perimeter is 6, which gives an approximation to
pi of 3. And, we divide the circle into 360 degrees. !
(0.618)(2.71)(3)=5.02434!
!
The decimal is. 24 15 04!
There are 24 hours in a day and the earth rotates through 360/24=15 degrees per hour. There
are four 7 day weeks in a month!
Conclusion
We can always round our molar mass to two places after the decimal. We can’t always round
better than that. Sometimes we can. The values in the matrices were all rounded to two places
after the decimal. I have been very careful in my rounding throughout all of the calculations, the
results were very interesting: It started with phi ( ) the golden ratio conjugate which is the
inverse of the golden ratio, the first three digits of Euler’s number e, and the approximation of pi
( ) of 3 as given by the regular hexagon which is where the side of a regular hexagon equals its
radius (if the sides are one, its perimeter is 6 and diameter is 2). Multiplying these we get
5.02434 and when we take its square root we get 24 15 04 the hours in a day, the degrees
through which the earth rotates in an hour, and the number of weeks in a month. Our matrices
result in molar masses that don’t exist but are in between those that exist such that they are
not horizontal or vertical in the periodic table, but diagonal (Figure 1)."
21.3607 = 4.621768
28.854 = 5.371592
ϕ = 0.618
e = 2.718
pi ≈ 3
5.02434 = 2.2415004
ϕ
π
of 8 20
"
Figure 1: Diagonal Elements That Don’t Exist (At
least in our Universe)
of 9 20
We can break up our square root into a sum of terms, where each term may by revealing using
Bakshali’s Method for approximating a square root (Figures 2 to 5).!
"
Figure 2: Bakshali’s First Estimate
of 10 20
"
Figure 3: Bakshali’s Second Estimate
of 11 20
"
Figure 4: Bakshali’s Third Estimate
of 12 20
"
Figure 5: Bakshali’s Fourth Estimate!
of 13 20
Venus
For some time I had been seeing 72 crop up. It is in 2001: A Space Odyssey when HAL, the
ship computer malfunctions and tells David Bowman and Frank Pool that the AE35 unit will fail
in 72 hours (3 days) and as such they will lose contact with Earth. I find this interesting because
HAL is silicon and germanium technology (presumably) and I had found silicon and germanium
very accurately connected to the Venus average orbital distance in AUs (Earth Sun separations)
which is 0.72. Venus has been of great interest to the Russians (they have sent several robotic
ships there) which is because according to Carl Sagan they are interested in it because it is our
sister planet (similar in size and mass) but she underwent a runaway greenhouse effect, which
means she is like a failed Earth. We note here in the Bakshali’s Fourth Estimate it converges on
7200 in the decimal. Four is the fourth planet Mars which I see as representing success in that
it is the terrestrial planet we can colonize. I wrote (Beardsley, Perfect Equations, 2021):!
If I consider my two books, Weird Arithmetic and Weird Calculus, and The Mathematical Nature
of Life, certain equations that I formed in them, while all of them are interesting, they stand out.
In the first book I looked at the connection of artificial intelligence to the planets. Out of all the
equations for the planets, Venus was the most dynamic in form, and the most accurate (Better
than 99%). This equation was:!
!
Where Si is silicon and Ge is germanium, the two principle semiconductor elements used to
make diodes and transistors, and are at the heart of artificial intelligence (AI) circuitry. The 0.72
is the amount of astronomical units in the Venus average orbital distance from the Sun, where
an astronomical unit (AU) is the average earth-sun separation. We can see the validity of this
equation as follows:!
!
Where Si and Ge are in in molar mass (grams/mole).!
Though I did not derive these equations, but guessed at them, it was an educated guess which
proceeded from the argument, that the first planet being the closest to the Sun, sets the idea in
motion, that idea being that its distance is in the simplest expression between Si, and Ge,
possible; the ratio between them. Thus for Mercury ( ) we have!
!
In astronomical units because we take an astronomical unit to be 1 AU at earth orbit, because
the earth is the one planets in the solar system that is highly hospitable to life.!
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
= 0.72
1
72.64
2
2(28.0855)(72.64) +
28.0855
3
72.64
1 +
28.0855
2
72.64
2
= 0.722995806
P
1
P
1
=
Si
Ge
of 14 20
To make our guess at the distance of the next planet, we first guess at the simplest idea r(n)=n.
Seeing this does not work we go the next simplest expression r(n)=2n. Seeing this does not
work we go one step higher in complexity and try . We see this does not work either
so we go one step of complexity beyond that and we try . And, we find this works.
But it must be tempered with a factor of 0.3 and and adjusted by 0.4. Thus we have the Titius-
Bode Rule for the distribution of the planets:!
!
!
To get the next equation for . Since we are dealing with a doubling effect we
guess it is , or . Which is close but a little too high. So we guess at something lower
and that it involves twice their product and something big, like the sum of their squares to
reduce the number to prevent the product from being too large. We guess that that value then
is . This is a little too low so we average the two to get exactly the result we need:!
!
Since the next planet, our Earth, must be at a greater value than Venus, and the uppercase
scenario for Venus is , we want to reduce 2SiGe by an amount less than the sum of
their squares, we reduce it by the difference of their squares and get for Earth:!
!
It takes a bit of doing, but the next planet ( ) is:!
!
The next location is the asteroids from 2.2 AU-3.2 AU. Since Mars is the last terrestrial planet
(solid), and the asteroid is a bunch of rocks that could not form into a solid planet and after the
asteroids we have the gas giants Jupiter, Saturn, Uranus, Neptune…and this represents a
flipping around point around the asteroid belt, I started counting again with a new pattern
starting with Jupiter as , and flipped the Earth equation and turned a minus sign to a plus to
obtain the Jupiter equation, which is a quadratic in its simplest form in the numerator, and a
product in its simplest form in the denominator, which is great because it is the first planet after
the asteroid belt and is hence:!
r(n) = n
2
r(n) = 2
n
r(n) = 0.4 + (0.3)2
n
n = − ∞, 0,1, 2,…
P
2
= Venus
2P
1
2
Si
Ge
2SiGe
Si
2
+ Ge
2
P
2
=
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
2SiGe
Si
2
+ Ge
2
P
3
=
2SiGe
Ge
2
− Si
2
P
4
= Mars
P
4
=
2SiGe
2
(Si − Ge)
2
(Si + Ge)
P
1
of 15 20
!
Now what happens is that a simple pattern forms. We simply multiply Jupiter by 2 to get
Saturn, then by four to get Uranus, and finally by six to get Neptune. We have:!
!
!
!
Thus we have the following table:"
P
1
=
Si
2
+ 2SiGe + Ge
2
SiGe
P
2
= Sat ur n =
2(Si + Ge
2
SiGe
P
3
= Uranu s =
4(Si + Ge
2
SiGe
P
4
= Neptune =
6(Si + Ge
2
SiGe
of 16 20
The lighter an element the more abundant, the heavier, the less abundant. Hydrogen is the
lightest element and the most abundant in the universe. Iron, for example is not that abundant
on earth, but it is heavy. However, something like silicon (the main component of sand SiO2)
and the most abundant in the earth crust, is relatively abundant in the universe. It is no wonder
that it is midway between hydrogen and iron, (1.01+55.85)/2=28.43 g/mol which is very close
to silicon Si=28.09. This may be why I find we can model a hypothetical protoplanetary disc
from the solar system formed in terms of silicon. I wrote (Beardsley, Perfect Equation, 2021):!
The Protoplanetary Disc
But, why describe the orbits of the planets in terms of AI Semiconducting elements? My
answer is to do something cosmic: there is great satisfaction in finding the connection between
two things that seem universes apart. And here I present a reason for looking at such a thing,
by considering the protoplanetary disc from which the planets formed. First we form a table of
the masses of the planets.!
of 17 20
!
Taking the protoplanetary disc as a thin disc we integrate from its center to the edge, with
density decreasing linearly to zero at the edge. Thus, if the density function is given by!
!
And, our integral is!
!
!
!
The mass of the solar system adding up all the planets yields!
!
That accounts for!
82% of the mass of the solar system not including the sun, that is, of the
protoplanetary disc surrounding the sun.!
Using germanium alone, we get,!
!
If we weight the mixture of silicon and germanium as 1/3 and 2/3, then we have!
!
Which is very close.!
93%!
This is all very good, because I only used the planets and asteroids.!
Si + Ge
2
=
2.33 + 5.323
2
= 3.8265g/cm
3
ρ(r) = ρ
0
(
1 −
r
R
)
M =
∫
2π
0
∫
R
0
ρ
0
(
1 −
r
R
)
rdrdθ
M =
πρ
0
R
2
3
π(3.8265)(7.4 × 10
14
)
2
3
= 2.194 × 10
30
gra ms
M = 2.668 × 10
30
gra ms
2.194
2.668
100 =
π(5.323)(7.4 × 10
14
)
2
3
= 3.05 × 10
30
gra ms
π(4.32467)(7.4 × 10
14
)
2
3
= 2.48 × 10
30
gra ms
2.48
2.668
100 =
of 18 20
Weighting silicon and germanium as 1/4 and 3/4 we have!
!
Which accounts for!
98%!
Of the mass of the solar system (very accurate).!
This mixture of 1/4 to 3/4 is a combination that exists in the Earth atmosphere which is
approximately the mixture of oxygen to nitrogen. The earth atmosphere can be considered a
mixture of chiefly O2 and N2 in these proportions:!
Air is about 25% oxygen gas (O2) by volume and 75% nitrogen gas (N2) by volume meaning
the molar mass of air as a mixture is:!
!
By molar mass the ratio of air to H20 (water) is about the golden ratio:!
!
I am not saying the solar system was a thin disk with density of the weighted mean somewhere
between silicon and germanium, but that it can be modeled as such, though if the
protoplanetary disk that eclipses epsilon aurigae every 27 years is any indication of what a
protoplanetary cloud is like, it is a thin disk in the sense that it is about 1 AU thick and 10 AU in
diameter (Kemp, Henson, Kraus, Beardsley, Carrol, Astrophysical Journal, January 1 1986
Letters). This around a star orbiting another star.!
The Babylonian Method
The oldest known method of determining a square root is the Babylonian method. We apply it
to our equation:!
!
The consecutive integers 2, 3, 4, 5, 6. It is actually!
=!
0.2634527818049960944743361359800!
We have!
!
π(4.4 . 57475)(7.4 × 10
14
)
2
3
= 2.623 × 10
30
gra ms
2.623
2.668
100 =
0.25O
2
+ 0.75N
2
≈ air
air
H
2
O
≈ Φ
1 −
Ga
As
= 1 −
69.72
74.94
= 0.26345
1 − .930592632140950 = 0.0694073678590
x
0
= 0.25 = 1/4
of 19 20
!
!
Which are five consecutive integers in the first five numbers after the second iteration and
Venus is the second planet, The consecutive integers are 2, 3, 4. 5, 6 are Venus, Earth, Mars,
Jupiter, Saturn. The third iteration:!
!
Are the consecutive integers 2, 3, 4, 5, 6, 7, 8 but the 7, 8 are separated from 2, 3, 4, 5. 6 by a
2, Venus, where this third iteration is earth (third planet). The consecutive integers 2, 3, 4, 5, ,6
7, 8 are up to eight there are eight planets in the solar system. It starts at Venus (2) and goes to
Neptune (8).!
If Venus I the second planet and is represented by 3 day which are 3(24hrs/day)=72 and!
Then since the earth is the third planet it might be represented by 4 days are 4(24hrs/day)=96,
then Mars being the fourth planet would be represented by 5(24hrs/day)=120.!
0.72/2=0.36 and arcsin(0.36)=21 degrees is approximately the earth tilt to the ecliptic (225
degrees) and 0.96/2=0.48 and arcsin (0.48)=28.68540201 are consecutive integers!
0, 1, 2, …4, 5, 6,…8!
There are 8 planets but 3 and 7 aren’t in the sequence are Earth and Uranus. We have
1.2/2=0.60 is approximately and arcsin (0.6)=36.87 degrees.!
!
Are the doping agent for!
"
x
1
=
1
2
(
0.25 +
0.069473678590
x
0
)
= 0.263814735718
x
2
=
1
2
(
x
1
+
0.069403678690
x
1
)
= 0.263453029382
x
3
=
1
2
(
x
2
+
0.069403678690
x
2
)
= 0.263452781080
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
= 0.72
ϕ = 0.618
1 −
Ga
As
1
Ge
2
2SiGe +
Si
3
Ge
1 +
Si
2
Ge
2
= 0.72
of 20 20
The Author
